Crick's "Frozen accident theory" of the genetic code explored by Ising models

Francis Crick proposed that the almost universal genetic code could be nothing more than a 'frozen accident'. The Ising model, widely used in statistical mechanics, is used to explore patterns which could achieve a phase transition mimicking the frozen accident. Codons are considered as nodes and amino acids as spins. Monte Carlo simulations of the 64-node genetic code models are carried out. Anti-ferromagnetic interactions or a combination of ferro and anti-ferromagnetic interactions can lead to stable, regular patterns resembling the genetic code. It is indeed found that the 64-node Ising system exhibits critical slowing down dynamics, compatible with a freezing process. These models aim to simulate the formation of patterns similar to the genetic code through physical freezing processes, providing insights into potential mechanisms and processes that may have contributed to the formation and evolution of the genetic code.